Let $f(x)=(x+2{)}^2-1$ with domain $x\ge -2,$ and define $g(x)=f(x-5)+3.$

1. State the range of $f.$

2. State a suitable domain for $g$ and give its range.

3. Find expressions for

   $$f^{-1}(x)\text{ and }{g}^{-1}(x)$$

   and sketch these two functions.

Sketch $y=f(x)$ to find its range.

Translate $y=f(x)$ to get a sketch of $y=g(x)$ - look at the $x$ axis to find the domain and the $y$ axis to find the range.

Take a look at the tutorial for inverse functions in this chapter if you're finding the last part tricky!